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3 years ago

Help with me 11 please

Mathematics

1 answer:

tino4ka555 [31]3 years ago

7 0

X + y + z = 27
x = 2z
y = 3 + z
2z + 3 + z + z = 27 ; 4z = 24; z = 6 youngest
x = 12 oldest
y = 9 middle one

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Given the definitions of f(x) and g(x) below, find the value of g( f(-5)).

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Answer:

we conclude that:

g(f(-5)) = 30

Step-by-step explanation:

Given

f(x) = x+9

g(x) = x² + 7x – 14

To determine

g(f(-5)) = ?

First, we need to find f(-5)

f(x) = x+9

substitute x = -5

f(-5) = (-5)+9

f(-5) = -5+9

f(-5) = 4

g(f(-5)) = g(4)

Now, we need to find g(4)

g(x) = x² + 7x – 14

substitute x = 4

g(4) = (4)² + 7(4) - 14

g(4) = 16 + 28 - 14

g(4) = 30

i.e.

g(f(-5)) = g(4) = 30

Therefore, we conclude that:

g(f(-5)) = 30

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3 years ago

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2 years ago

Find the values of λ for which the determinant is zero.

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Answer:

Determinant are special number that can only be defined for square matrices.

Step-by-step explanation:

Determinant are particularly important for analysis. The inverse of a matrix exist, if the determinant is not equal to zero.

How to find determinant

For a 2×2 matrix

$det ( \left[\begin{array}{cc}x&y\\a&z\end{array}\right] ) = xz-ay$

For a 3×3 matrix

we first decompose it to 2×2

$det (\left[\begin{array}{ccc}k&l&m\\o&p&q\\r&s&t\end{array}\right] )\\\\= k*det(\left[\begin{array}{cc}p&q\\s&t\end{array}\right] ) - l*det(\left[\begin{array}{cc}o&q\\r&t\end{array}\right] ) + m*det(\left[\begin{array}{cc}o&p\\r&s\end{array}\right] ) \\\\=k(pt-sq) - l(ot-rq) + m(os-rp)$

Example

Find the values of λ for which the determinant is zero

$\left[\begin{array}{ccc}s&-1&0\\-1&s&-1\\0&-1&1\end{array}\right]$

$det(\left[\begin{array}{ccc}s&-1&0\\-1&s&-1\\0&-1&1\end{array}\right])\\\\= s*det(\left[\begin{array}{cc}s&-1\\-1&1\end{array}\right] ) - (-1)*det(\left[\begin{array}{cc}-1&-1\\0&1\end{array}\right] ) + 0*det(\left[\begin{array}{cc}-1&s\\0&-1\end{array}\right] )\\\\= s(s(1)-(-1*-1)) - (-1)(-1*1 - (-1*0)) + 0\\= s(s - 1)) + 1(-1 + 0) \\=s^{2} -s-1$

Equating the determinant to zero

$s^{2} -s-1 =0\\$

s = $\frac{1}{2}$ * (1 ±5 )

s = 1.61 or -0.61

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3 years ago